SUMS OF UNITS IN SOME CLASSES OF NEAT RINGS

Document Type : Original Manuscript

Author

Department of Mechanical Engineering, University of Shohadaye Hoveizeh Campus of Technology, Shahid Chamran University of Ahvaz, P.O. Box 64418-78986, Susangerd, Iran.

Abstract

A ring R is said to be clean if every element of R is a sum
of an idempotent and a unit. A ring R is a neat ring if every nontrivial
homomorphic image is clean. In this paper, first, it is proved that every
element of some classes of neat rings is n-tuplet-good if no factor ring
of such rings isomorphic to a field of order less than n + 2. Also by considering
the structure of FGC rings, it can be proved that some clasess of FGC
rings are n-tuplet-good.

Keywords

References

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Journal of Algebraic Systems
Volume 10, Issue 1
September 2022
Pages 147-153

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